MathDB

5

Part of 2017 Tuymaada Olympiad

Problems(2)

Congruence

Source: Tuymaada 2017 Junior Level

7/18/2017
BLBL is the bisector of an isosceles triangle ABCABC . A point DD is chosen on the Base BCBC and a point EE is chosen on the lateral side ABAB so that AE=12AL=CDAE=\frac {1}{2}AL=CD . Prove that LE=LDLE=LD .
Tuymaada 2017 Q5 Juniors
geometry
quadratic trinomial with integers 2 of it's coefficients

Source: Tuymaada 2017 Seniors Q5 (day 2 P1)

9/26/2017
Does there exist a quadratic trinomial f(x)f(x) such that f(1/2017)=1/2018f(1/2017)=1/2018, f(1/2018)=1/2017f(1/2018)=1/2017, and two of its coefficients are integers?
(A. Khrabrov)
QuadratictrinomialInteger Polynomialalgebra